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Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, commutative rings, module and ring theory, and topological algebraic structures-providing more than 600 current references and 570 display equations for further exploration of the topic.

Abelian groups. --- Rings (Algebra) --- Modules (Algebra) --- Commutative groups --- Group theory --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Algebraic rings --- Ring theory --- Algebraic fields

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Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches. .

Group theory --- Ordered algebraic structures --- Algebra --- algebra --- wiskunde